"""
Algorithm to find a maximal (not maximum) independent set.
"""
import networkx as nx
from networkx.utils import not_implemented_for
from networkx.utils import py_random_state
__all__ = ["maximal_independent_set"]
[docs]@py_random_state(2)
@not_implemented_for("directed")
def maximal_independent_set(G, nodes=None, seed=None):
"""Returns a random maximal independent set guaranteed to contain
a given set of nodes.
An independent set is a set of nodes such that the subgraph
of G induced by these nodes contains no edges. A maximal
independent set is an independent set such that it is not possible
to add a new node and still get an independent set.
Parameters
----------
G : NetworkX graph
nodes : list or iterable
Nodes that must be part of the independent set. This set of nodes
must be independent.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
Returns
-------
indep_nodes : list
List of nodes that are part of a maximal independent set.
Raises
------
NetworkXUnfeasible
If the nodes in the provided list are not part of the graph or
do not form an independent set, an exception is raised.
NetworkXNotImplemented
If `G` is directed.
Examples
--------
>>> G = nx.path_graph(5)
>>> nx.maximal_independent_set(G) # doctest: +SKIP
[4, 0, 2]
>>> nx.maximal_independent_set(G, [1]) # doctest: +SKIP
[1, 3]
Notes
-----
This algorithm does not solve the maximum independent set problem.
"""
if not nodes:
nodes = {seed.choice(list(G))}
else:
nodes = set(nodes)
if not nodes.issubset(G):
raise nx.NetworkXUnfeasible(f"{nodes} is not a subset of the nodes of G")
neighbors = set.union(*[set(G.adj[v]) for v in nodes])
if set.intersection(neighbors, nodes):
raise nx.NetworkXUnfeasible(f"{nodes} is not an independent set of G")
indep_nodes = list(nodes)
available_nodes = set(G.nodes()).difference(neighbors.union(nodes))
while available_nodes:
node = seed.choice(list(available_nodes))
indep_nodes.append(node)
available_nodes.difference_update(list(G.adj[node]) + [node])
return indep_nodes